Mathematics

In the last years, the exponential diffusion of machine learning algorithms has contributed to improving already consolidated procedures, as well as allowing the creation of new frameworks, also in the field of data-driven and reduced order modeling. In particular, the neural networks, thanks to their approximation capability, have enabled the treatment of complex nonlinear models, maintaining a very limited computational cost during the inference of these models.
In this presentation, we present some of the enhancements obtained by employing neural networks to overcome the limitations of standard techniques like 1) an automatic snapshot shifting to solve the weakness of proper orthogonal decomposition in advection-dominated problems, 2) a multi-fidelity approach to improve the accuracy of a generic data-driven reduced order model and 3) the development of continuous convolutional filter to reduce the dimensionality with unstructured data.